Optimal steady-state temperature distribution for a phased array hyperthermia system

A method is presented for the evaluation of optimal amplitude and phase excitations for the radiating elements of a phased array hyperthermia system, in order to achieve desired steady-state temperature distributions inside and outside of malignant tissues. Use is made of a detailed electromagnetic and thermal model of the heated tissue in order to predict the steady-state temperature at any point in tissue. Optimal excitations are obtained by minimizing the squared error between desired and model predicted temperatures inside the tumor volume, subject to the constraint that temperatures do not exceed an upper bound outside the tumor. The penalty function technique is used to solve the constrained optimization problem. Sequential unconstrained minima are obtained by a modified Newton method. Numerical results for a four element phased array hyperthermia system are presented.